4 hat #riddle

The explanation
As vexing as it might seem, the “four hats” riddle can be solved using the process of elimination. And two of the prisoners (prisoners A and B) can be eliminated right off the bat. That’s because neither can see any of the other prisoners, so neither possesses any information with which to make an educated guess.

That leaves just prisoners C and D.
Prisoner D might seem the obvious choice because he can see the hats of both prisoners C and B in front of him, whereas prisoner C can see only the hat of prisoner B. Indeed, if prisoners B and C were wearing the same color hat, then prisoner D would have known immediately that he was wearing the other color. However, in this scenario, prisoners B and C are wearing different colored hats. Seeing this, prisoner D, in effect, has no more information than prisoners A and B. Accordingly, he too is left in the position of being unable to make an educated guess.

As for prisoner C, prisoner D’s silence is all the information he needs. Had prisoner C and prisoner B been wearing the same color hat, prisoner C surmises, then surely prisoner D would have piped up with the answer already. Accordingly, at the end of the 10 minutes, prisoner C deduces that he and prisoner B must be wearing different color hats. And since prisoner C can see that Prisoner B is wearing a white hat, then prisoner C knows that he must be wearing a black hat.
The answer
Prisoner C (who calls out that he is wearing a black hat).